David Cameron has warned Vladimir Putin to heed the "lessons" of Russia's aggression in Ukraine after the president vowed to keep defying the West.

The Prime Minister said Moscow's economy was in "serious" trouble after being hit by a slump in oil prices and sanctions from the EU and US. And he insisted the pressure would not be lifted until Mr Putin stopped flouting the basic rules of the international community.

The comments came at the conclusion of the European Council summit in Brussels, which saw fresh punitive measures imposed by members. With effect from Saturday, the ban on investment in Crimea is being widened to target Russian Black Sea oil and gas exploration.

The move comes on top of a range of other restrictions imposed by the EU and US on key banks, corporations and officials. But in his annual set-piece press conference earlier, Mr Putin showed little sign of being ready to back down - declaring that Russia would not be "chained".

The premier accused the West of trying to turn Moscow into a "stuffed bear", and promised it would weather the current turmoil that has seen the rouble crash. Attributing 25% of Russia's problems to international sanctions, Mr Putin compared his annexation of Crimea with the US "chopping" Texas from Mexico.

"Do they want our bear to become a stuffed animal?" he said. "Maybe our bear should sit quietly, not chasing any piglets around, but just eating honey and berries. Maybe they should just leave him alone? They will not.

"They are trying to put it on a chain. And as soon as they do it they will tear his teeth and claws out."

But Mr Cameron said the EU had been "unanimous" that sanctions would be maintained until Russia "changes its behaviour and stops the aggression in Ukraine".

"I think the state of the Russian economy is serious, and I think that something very important is being made clear here, which is that if you want to have full access to the international capital markets you cannot behave in a way that flies in the face of the international rules and how to behave towards other countries," he said.

"That is the real lesson here. And I have always said, the door is alwasy open if Russia changes its behaviour, if it allows the Ukrainian people to exercise their choice, their sovereignty, and decide their future.

"If it takes Russian troops out of Ukraine, and it obeys all the strictures of the Minsk agreement, these sanctions can go. But until that happens these sanctions should not go and there was a very clear and unanimous and unified view in the EU tonight."

The meeting in Brussels was the first overseen by new European Council president Donald Tusk, formerly prime minister of Poland. Before the talks got under way, Mr Cameron held bilateral meetings with Mr Tusk's successor as Polish leader, Ewa Kopacz, and Bulgarian PM Boyko Borisov.

Mr Cameron's drive to renegotiate Britain's relationship with the EU ahead of an in/out referendum mooted for 2017 was confined to the margins. But French president Francois Hollande is thought to have warned the PM that the price for keeping the UK in the union keeps rising, and he does not accept the need for treaty change.

The leaders also considered new European Commission president Jean-Claude Juncker's plan to mobilise 315 billion euros (£249bn) in extra investment - largely from the private sector - over three years. And they have sought to make progress on a major trade deal with the US - known as the Transatlantic Trade and Investment Partnership (TTIP) - despite concerns in the UK that it could force public services to offer contracts to foreign companies.

Mr Cameron, who has dismissed suggestions the NHS could be at risk from the proposed deal, said: "We have had a good meeting here on the economy. We support the investment plan that's been announced and the projects we have for British infrastructure can benefit from that plan.

"But I have also been pushing hard and successfully for making sure we have an ambitious trade agreement with America, making sure we complete the EU single market. "Both of those aims have been strongly endorsed here."